Don Ellis - Quarter Tones: A Text with Musical Examples, Exercises and Etudes

QUARTER
TONES

A text with musical examples, exercises and etudes

by Don Ellis

This book is dedicated to
HAROLD BRANCH
who provided the original suggestion for
doing such a work and gave the stimulus

necessary for bringing it into being.

© COPYRIGHT 1975 BY HAROLD BRANCH PUBLISHING, INC.
International Copyright Secured All Rights Reserved
Published at 42 Cornell Drive, Plainview, Long Island, New York 11803

TABLE OF CONTENTS

INTRODUCTION.

CHAPTER 1 - The Background-Equal Temperament.
CHAPTER 2 - The History of Quarter Tones.

CHAPTER 3 - The Notation of Quarter Tones.

CHAPTER 4 - My Personal Interest

CHAPTER 5 - Fingering Charts.

CHAPTER 6 - Basic Quarter Tone Scales.

CHAPTER 7- Exercises for Dexterity and Ear Training
CHAPTER 8 - Melodic Studies Using Quarter Tones.

BIBLIOGRAPHY.

QUARTER TONES

INTRODUCTION

Ever since man's earliest days music has played an important part in his life,
and just as man has continually worked to expand his horizons in other fields,
so has he struggled to increase the means and expressive power of his music.

Today, most of the music one hears in our (Western) culture, is based on the
equal tempered scale (i.e., twelve equally spaced notes to an octave). How-
ever, since jazz and black music burst on the public consciousness around the
turn of this century, the dominance of the equal tempered system has been
seriously challenged.

The musics of jazz, blues and rock and roll, with their use of "blue" notes,
bent tones, melismas and glissandi introduce pitches not found in equal tem-
perament and anyone familiar with these forms of music knows the tremendous
power and excitement these notes"in the cracks of the piano" can generate.

There is a whole new exciting world to be discovered (and rediscovered) in the
area of intervals and intonation. The use of quarter tones is a step in this di-
rection. For the future there is much experimentation, research, and just
plain making of music to be done.

It is my hope that this book will be of help to persons who are interested in
exploring new possibilities.

CHAPTER 1

THE BACKGROUND-EQUAL TEMPERAMENT

First of all, to put things into a historical perspective, remember that our
system of twelve equal tempered notes to the octave is a relatively recent de-
velopment in the history of music, the first equal tempered organ being tuned
in Hamburg, Germany in 1688. Before this the music of the world had many
different systems of tuning. The earliest of which we have evidence is that of
Ling Lum, a court musician under Emperor Huang-ti, living in the 20th Century
B. C. in China, who worked out a mathematical formula for the pentatonic scale.

Marin Mersene (1588-1648), the French monk, mathematician and physicist,
was the first Westerner to give the correct solution for equal temperament.’
However, it was not until forty years after his death that the first organ was
tuned with his formula for equal temperament (at Hamburg in 1688).

" See Harry Partch, Genesis of a Music: Monophony, (Madison, Wis., Univer-
sity of Wisconsin Press, 1949) for an excellent history of intonation.

*Ibid., p.256.
Joseph Schillinger, in The Schillinger System of Musical Composition, Vol.1,
(New York: Carl Fischer, Inc., 1941), p. 102, credits Andreas Werckmeister
with developing the mathematical expression for equal temperament (12,3 )
in Germany in 1691. The frequencies are logarithmically related.

One big (and perhaps the only) advantage of equal temperament was that it
allowed modulation into all twelve keys. This was a tremendous achievement
but it meant that we sacrificed pure (in tune) ratios of pitch to having every
interval (slightly) out of tune. For a culture such as ours, which was becom-
ing more and more harmonically dominated and less and less melodically
oriented, this was a distinct advantage. When you have only two basic scales
(major and minor) out of which to construct melodies, it is almost impera-
tive that you modulate into other keys if for no other reason than to escape
boredom. However, even multiplying the two basic scales by each of the 12
chromatic possibilities (which still gives only two basic scales) seems rather
colorless when compared to the richness of a musical culture such as India,
for example, which has 72 basic Thats ("scales") and 34, 848 possibilities for
scales (of which 150 to 200 are in current use) based on only one fixed tonic I

Today, due in no small part to equal temperament, our ears have become
dulled to hearing the subtle nuances of pitch that are readily discernible to
people in other cultures. We paid a big price for this ability to modulate
freely.

My original interest in quarter tones was not just to have 12 more keys (24 to
the octave, as opposed to the current 12) to modulate into, or to compound the
problems of equal temperament. I wanted to be able to hear other, newer,
fresher pitch ratios, some of which happen to come closer to just intonation
(i.e., pure ratios) . I've also found I can achieve startlingly new effects with
blue notes by means of quarter tones.

CHAPTER 2

THE HISTORY OF QUARTER TONES

Going back in recorded history we find that microtones (any intervals smaller
than a semi-tone) have long been a structural part of Asian music. In the West
we know that Greek music during the period of Euripides (circa 480-06 B.C.)
included quarter tones.-° It is also probable that several of the "ornamental"
neumes of Gregorian chant involved quarter tones.“

One of the most interesting musical mavericks of all time was Nicolo Vicentino
(1511-1572) . He used a harpsichord type of instrument called the "arcicembalo",
a microtonic instrument (circa 1550) with 31 tones to the octave in six banks
of keys. His avowed purpose was to revive ancient Greek genera and his in-
strument gave all the diatonic, chromatic enharmonic genera of ancient Greek
theory.”

Willi Apel, Harvard Dictionary of Music. 2d Ed. (Cambridge, Massachusetts:
The Belknap Press of Harvard University Press, 1972), Microtones p. 527,
and Greece II, p. 352.

“Tbid., Neumes I, p.571, The "Gradual of Montpellier" illustrates the practi-
cal use of quarter tones in the 11th Century.

“Ibid., p. 48.
Partch, p. 251.

His enharmonic system divided the whole tone into five parts.° It is significant,
perhaps, that most of the musicians of his time were violently opposed to his
experiments.

Charles Luython (1556-1620) built a simplified instrument ("cymbalum univer-
sale") with 18 keys to the octave which allowed modulation to all keys without
resorting to the compromise of equal temperament.’

Lemme Rossi (1601-1673) gave numbers for string lengths of equal quarter
tones, perhaps for the first time.® At the end of the Seventeenth Century
Christiaan Huygens suggested a 31-part division of the octave, allowing modu-
lation in just intonation.” (Adriaan Fokker has advocated the same 31-note
scale in this Century.)’°

°Gustave Reese, Music in the Renaissance (New York: W.W. Norton & Com-
pany, Inc., 1959), p. 328.

"Harvard Dictionary, 2d Ed., p.49.

8 J. Murray Barbour, Tuning and Equal Temperament, (East Lansing, Michigan:
Michigan State College Press, 1953), pp. 201, 220. Partch, p. 299.

° Harvard Dictionary, 2d Ed., p. 527.

“Tbid., p. 449.

A Syrian Theorist in the Nineteenth Century, Michael Meshaquah, advocated
dividing the octave into 24 equal parts.11 Joseph Yasser, in his book, The
Theory of Evolving Tonality (1932) suggests the division of the octave into 19
equal parts.

Since its introduction in 1688 equal temperament became the main force in
musical intonation in the West and overshadowed all else. But musicians be-
came restless, and in 1895 Julian Carrillo wrote a string quartet using quarter
tones, and in the early 1900's Charles Ives1* began writing in quarter tones.
A theory of third tones was developed by Ferruccio Busoni. 1°

! Hermann Helmholtz, On the Sensations of Tone, (New York: Dover Publica-
tions, Inc., 1954), p. 264. Partch, p. 298.

'? Charles Ives (edited by Howard Boatwright), Essays Before a Sonata and
Other Writings, (New York: W. W. Norton & Company, Inc., 1961), p. 105.
Ives has some very provacative things to say about quarter tones and con-
structing harmonies out of them, suggesting among other things that quarter
tone harmonies sound better when there are at least four notes to a chord,
rather than three, since 3-tone chords tend to sound more like previously
familiar chords.

13Ferruccio Busoni, Sketch of aNew Esthetic of Music, (New York: G. Schirmer
Inc., 1911).

10

I. Vysnegradsky wrote "Dithyramb" in 1926 and "Prelude and Fugue" in 1929
using quarter tones, and in 1930 Hans Barth wrote a "Concerto for Quarter
Tone Piano and Strings."

Perhaps the most noted composer of quarter tones, the Czech, Alois Haba,
wrote many pieces that used quarter and sixth tones. Harry Partch (1901-) has
divided the octave into 43 unequal parts and written many provocative works,
some of which are currently available on record.'* Recently younger com-

posers, such as Krzystof Penderecki, have become interested in the possibili-
ties of quarter tones.

The first patent on a quarter-tone piano was in 1892 by G. A. Behrens-Sene-
galden.'> In 1902 Max F. Meyer had a harmonium that played quarter tones
and he developed a system of music that stated the case for using ratios as
common musical terms (for the purpose of clarity).’°

4 See p. 19.
Harvard Dictionary, 2d Ed., p. 528.

'°Max F. Meyer, The Musicians Arithmetic: Drill Problems for an Introduction

to the Scientific Study of Musical Composition, (Columbia, Missouri: Univer-
sity of Missouri Press, 1929) .

11

Indian music for many centuries has had a system of 22 notes (srutis) to the
octave. For a fascinating description of this, and many other aspects of Indian
music, please refer to the recently re-published book, The Music of Hindostan

by A. H. Fox Strangways.1’

Ernst Toch, in his book, The Shaping Forces in Music,18 makes the fascinating
suggestion that masters such as Beethovenand Brahms might have used quarter
tones in some of their music to good effect! He goes on to give examples of
just how they might have done this. He also states a case for making quarter
tones intelligible, logical and " beautiful."

'7 4. H. Fox Strangways, The Music of Hindostan, (Oxford: at the Clarendon
Press, 1965; orig. 1914) .

18 Ernst Toch, The Shaping Forces in Music, (New York: Criterion Music
Corp., 1948) .

12

CHAPTER 3

THE NOTATION OF QUARTER TONES

Many systems have been devised for notating quarter tones:

EXAMPLE 1.7”

+
4 _ sharped note to be played
f, 5 5 S f ~ a quarter tone high
% ¢ i d M4 \# _ sharped note to be played

a quarter tone low

4
At he L 4b _ flatted note to be played
a quarter tone high

y
Bo be eM é tb . flatted note to be played
a quarter tone low

20 471 natural note to be played
bs os dls S r i a quarter tone high

1
. natural note to be played
as v ¢ d P 4 a quarter tone low

22
EXAMPLE Qs specteste gegen!

Example II shows the notation of quarter tones and the beginning of Haba's
Op. 9.

Js | _s Se

aR Se Se ee ee |
(a WU ey FO GE a ER
a A OE PY PT . 2

Gardner Read, Music Notation, 2d Ed., (Boston: Allyn and Bacon, Inc.,
1969), p. 145.

?°fusical Quarterly, Contemporary Art Music in Persia, (New York: G.
Schirmer, Inc., Vol. LI, No. 4, October 1965), p. 640 (Ali Naqi Vaziri-

b. 1886).

7! Pavel Blatny, The Study for 1/4 Tone Trumpet, Dedicated to Don Ellis,
May 1965, Brno-Czechoslovakia.

Willi Apel, Harvard Dictionary of Music, (Cambridge, Massachusetts: Har-
vard University Press, 1955), p. 619.

13

23
EXAMPLE III.

1. Haba system for quarter tones found in his String Quartet op. 12, no. 2.
2. Haba - for sixth tones, found in his String Quartet op. 81, no. 11.
3. Another fairly common system for quarter tones used by Krystof Penderecki

in Anaklasis (1959/60) .

To me the simplest and clearest form of quarter tone notation is the simple use
of arrows:

* Harvard Dictionary, 2d Ed., p. 527

14

This has proved to be easy to read and practical. With stringed instruments,
notes both quarter tones sharp and flat may be used. However, in the case of
the quarter-tone trumpet, it is much easier and more practical to notate every
thing with quarter tones flat (arrows pointing downward). Since the fourth
valve, when depressed, lowers every other combination of the first three by a
quarter tone, all of the 24 quarter tones of the chromatic scale can be notated
in this manner, and it presents no difficulty to the trumpet player in sight
reading.

According to a system worked out by Alexander J. Ellis (1814-1890), the
famous annotator to Hermann L. F. Helmholtz, each of the equally spaced 12
notes of the chromatic scale are equal to 100 cents, and there are 1200 cents
to an octave. Therefore, a quarter tone would be equal to 50 cents. (Mathe-
matically, cents are a logarithmic measurement.) The following chart shows
the relationship between quarter tones, equal temperament and just intonation.”

4 See also Partch, p. 303.

CENTS OUT OF TUNE

12 TONE 24 TONE IN COMPARISON TO
RATIOS CENTS EQUAL EQUAL JUST INTONATION
Ail 1200 1200 1200* 0
160/81 1178.5
64/33 1146.8 1150* +32
40/21 ILIS5
15/8 1088.3 1100 1100 #117
11/6 1049.4 1050* +.6
20/11 1035.0
9/5 1017.6
16/9 996.1 1000 1000* +3.9
7/4 968.8 -18.8
12/7 933.1 950 +16.9
27/16 905.9 900 900 -5.9
5/3 884.4
18/11 852.6 850* -2.6
8/5 813.7 800 800 -13.7
11/7 7182.5
14/9 764.9 750 -14.9
32/21 Teoee
3/2 702.0 700 700* -2.0
40/27 680.5
16/11 648.7 650* +1.3
10/7 617.5
ie 582.5 600 600 ae We
11/8 bee 350" -1.3
21120 x19 5
4/3 498.0 500 500* +2.0
21/16 470.8
9/7 435.1 450 +14.9
14/11 417.5
5/4 386.3 400 400 +13.7
11/9 347.4 350* 4+2..6
6/5 315.6
31/27 294.1 300 300 oso
7/6 266.9 250 -16.9
8/7 2a 1.2
9/8 203.9 200 200* -3.9
10/9 182.4
11/10 165.0
12/11 150.6 10" -.6
16/15 111.7 100 100 -11.7
21/20 84.5
33/32 S32 50
81/80 ZL
1/1 0 0 0
- = FLAT
+= SHARP

** = most in tune
Partch. page 303, for further scales.

16

Note that the quarter-tone scale comes close to pure intervals in the notes in-
dicated above by asterisks on the chart. The other notes are "out of tune" in
the exact relationship to the extent that they vary from the pure (just) ratios.
(For many interesting scales approaching just intonation which can be derived
from this chart see Pages 33-37.)

To point out the value of quarter tones in today's context let me quote from
Harry Partch, an advocate of just intonation, and one who is certainly no friend
of quarter tones.

"As a temporary expedient, as an immediately feasible method
of creating new musical resources, 'quartertones' are valuable.
That they are comparatively easy to obtain is evidenced by the
many composers and performers who have used them: Alois
Haba, with three piano manuals, the first and third of which played
identical tones, and the second a 'quartertone’ higher than the
other; and Mildred Couper, with two pianos, the second tuned a

'quartertone’ above the first."

cae Partch, p. 302.

17

MY PERSONAL INTEREST

My first serious interest in quarter tones dates from January 1965, when I be-
gan talking to Perry Pirone, a brass mouthpiece maker and repairman on the
east coast, about the possibilities of constructing a trumpet that would be able
to execute accurate quarter tones. Perry told me that it would be relatively
easy to construct such a trumpet and all that was necessary was some type of
valve that would lower the other combinations by a quarter step, and that the
tubing for this valve would be exactly half as long as the tubing on the second
valve of the trumpet (the half-step valve) . I was so delighted with this simple
solution to what I had thought would be a rather complex problem that I called
the Frank Holton Company right on the spot and asked them if they would be

interested in making such a trumpet for me.

They were interested, but I got no results until March 1965, when in one of
those amazing historical coincidences I received a communication from Eric
Vogel, the German jazz critic, telling me of Pavel Blatny, the noted Czecho-
slovakian jazz and symphonic composer, and his experiments with a quarter-

tone trumpet.

Evidently there was atrumpet player on the other side of the world (in Czecho-
i-jvakia) who had developed a quarter-tone trumpet, and Mr. Blatny had writ-
ten a piece for it. I was sent a tape of this piece and was very impressed. I
—imediately called the Holton Company back and told them that somebody had
already developed a quarter-tone trumpet behind the Iron Curtain. It was only
a short time from that moment until I was presented with my first quarter-tone

in September 1965!

18

I have never seen the trumpet used by the Czech musician, so I don't know how
it is constructed, but my quarter-tone trumpet has a fourth valve, which is
played by the little finger, and it lowers any combination of the first three by a
quarter step. I found the quarter tones on the trumpet very easy to play, and
to my delight, I found that the trumpet played better than any other instrument
I had ever owned. I was apprehensive that adding the fourth valve might destroy
the balance of the trumpet, but was pleased to see that it seemed to open up the
regular horn and make it play even better. I immediately began playing this
trumpet on all my jobs, including the commercial jobs and record dates I was
doing in the Los Angeles area at the time.

The first real exposure that the quarter-tone trumpet received was at the
Monterey Jazz Festival on September 20, 1966, when my Big Band and I made
our debut. This is documented on record and is still available:

Live at Monterey, Pacific Jazz ST-20112

Later on I outfitted my whole trumpet section with quarter-tone trumpets and
wrote a piece called "Headquarters." This piece was never recorded. How-
ever, we have played it for some radio broadcasts in Europe. We did record
several pieces on the New Don Ellis Band Goes Underground album (Columbia
CS-9889) which use quarter tones. Even though basically a rock context, you
can hear the whole band, and especially the trumpet section, playing quarter
tones.

I have been able to find two recordings that are currently available and are ex-
cellent examples of quarter tones and microtones:

Concertino Pour Piano En 1/3 De Ton

Julian Carrilo (Modern Music Series, Gravure Universelle, Philips 839.272
DSY), and

New Music in Quarter-Tones,

which has works by Charles Ives, Calvin Hampton, Donald Lybbert, Teo Macero
(Odyssey 32 16 0162) .

19

Also, Harry Partch has recently recorded some fine works on Columbia:
Delusions of the Fury, M2 30576
The World of Harry Partch, M31227

And, of course, on all my records I make use of the quarter-tone trumpet:
Live at Monterey, Pacific Jazz ST 20112
Live in [3 73/4 Pacific Jazz ST 20123
Electric Bath, Columbia CS 9585
Shock Treatment, Columbia CS 9668

Autumn, Columbia CS 9721

Don Ellis at Fillmore, Columbia G30243

Tears of Joy, Columbia G30927

Connection, Columbia KC31766

Soaring, MPS/BASF MB25123

Haiku, MPS/BASF MB25341

I believe we are at a musical crossroads. New developments in melody, rhythm

and harmony are needed. But more importantly, our whole system of intonation
and tonality must be looked at and re-evaluated, and a fresh approach devised.
The surface has barely been scratched. For the first time in history we are at a
point where new technological developments make possible the instant testing of
theories whichin previous generations would have taken years to train musicians

to be able to perform. Today, with electronic music, development can occur at
a much faster rate.

20

I have invented a new type of electronic keyboard instrument which I believe
will answer the needs of composers and musicians to be able to experiment
with new concepts of harmony and intonation. In the next few years I hope to
find an instrument manufacturer to mass produce this instrument. This will
enable composers and musicians to try out new theories of intonation and har-
mony without having to spend tedious hours building instruments or retuning

existing instruments to be able to cope with the new theories.

What has been done with quarter tones so far (including my own work) has been
basically decorative rather than organic. Hopefully, instruments that will be
developed inthe next few years will open the way for new, exciting experiments
into the infinite world of tonality and intonation. It is my hope that the new
musics that are derived from theories yet to be invented will not just sound

different or strange, but be new, fresh, exciting and. beautiful!

ier

CHAPTER 5
FINGERING CHARTS

THE QUARTER- TONE TRUMPET

On the four valve quarter-tone trumpet the first three valves operate exactly
like the normal three valve trumpet. The fourth valve lowers any combination
of the first three by a quarter of a tone. Because this is the way the trumpet
operates, I have found it expedient to always indicate quarter tones for the
trumpet with the arrow downward. This means the trumpeter has only to play
whatever note he sees, whether natural, sharped or flatted, and if the arrow

points downward in front of it he merely depresses the fourth valve to get the
proper tone.

TRUMPET

© COPYRIGHT 1975 BY HAROLD BRANCH PUBLISHING, INC,
International Copyright Secured All Rights Reserved
Published at 42 Cornell Drive, Plainview, Long Island, New York 11803

22

0004

1004 1000 0204 0200 0000 1204 1200

1004 1000 0204 0200 0004 0000 1004 1000

SE. 1 See

0204 0200 0004 0000 0234 0230 Pa i 1200
J .) 4) U So

1004 1000 0204 . 0200 0004 0000

_
bo
=)
>
_
no
oO
oO

1004 1000 0204 0200 0004 0000 1004 1000
her sie wolfe gate! oe = ‘2 =

0204 1000 1004 0000 0004 ~—S— 0200 0204 ~—- 1000
veo ° Ya * Ye be Ybe o
1004 1200 1204 0000 0004 ~—S 0200 0204 —«- 1000
+2 bo vba 2 +o 2 Yo ba

23

0200

0004

0000

2304
Vbe

1204 2300
be

Yeo

1200

tba

0004 0200 0204 1000

0000

1004

1204 0000 0004 0200 0204 1000

1200

0004 0200 1000
Sa SSS Ge SSS OF See ee Se
o ced pe

1034-1230 = 1234
a
1s bs ybo

1030
_———4
o

24

TROMBONE

Playing quarter tones on a trombone is a relatively simple matter. It means that one has
another position half way between the original seven positions on trombone. Since it is
easy for the trombone to play a quarter tone sharp as well as a quarter tone flat, I have
indicated the ascending scale to be played with the quarter tone sharp and the descending
scale with the quarter tones flatted.

71/2 7 61/2 Ss "S172 | 5 41/2

25

26

41/2

3 1/2

Yo

31/2

21/2

11/2

11/2

5 1/2

41/2

41/2

31/2

3

21/2

% 1/2

6 1/2

6

5 1/2

3 1/2

21/2

2

11/2

71/2

(3

6 1/2

6

5 1/2

41/2

D -

SAXOPHONE

A student and friend of mine, Wes Brown, has developed a device for saxophone
that would convert any saxophone into a quarter-tone instrument. We have not
found an instrument company as yet who is interested enough to begin manufac-
turing the device. Suffice it to say it works similarly to the way the quarter-
tone trumpet works by altering the normal combinations of fingerings.

Another friend, a brilliant virtuoso, concert and jazz saxophonist, Trent
Kynaston, has worked out a system of fingerings for the standard saxophone
with approximate quarter tones. Trent comments:

"There are quarter tone fingerings in between all notes, but those

in brackets are very impractical. Between G and Ab the fingering

is by means of a half-whole because of the articulated G# key. The

same problem occurs in the low range of the instrument.

The fingerings all give approximate pitches; some embouchure
adjustment is necessary. Each saxophonist attempting the finger-
ings should experiment with slight alterations of finger combina-
tions as pitch will vary from alto to tenor and baritone as well as
individual instruments in terms of how they are adjusted. The
diagram explains the fingering chart."

28

@ desired pitch

0 slightly for
3
8

0 < lower

0

ooo ooo

Nn
Neal

ceo ooo

oO
~

av
“7

ooo ooo

eeecee

@ec ecco

eeo eee

@co coe

coe ece
oO

eee ece

Octave Key

SAXOPHONE DIAGRAM

29

30

STRINGS

For an unfretted stringed instrument, playing quarter tones is an easy matter: just flat-

ten or sharpen the note by a half position. I have written out a chart for the treble clef
with the quarter tones sharp ascending and the quarter tones flat descending. The bass

clef stringed instruments may refer to the trombone chart.

6|

2

2

$1 |

31

6! |
>

911]
A

oll

be

be

Y 2

2

,
Sy Sa FSR Ci REE FLA SS GE Be Sey SS ES CS a Pa Pee
a

7

BE ) (SSS Ser ee ee f+ lee ee Se

32

KEYBOARDS

As yet there are no practical quarter tone keyboards in general use. However,
as I mentioned earlier, I have invented such an instrument and hope the day
will come soon when an instrument manufacturer will mass produce it. In the
meantime, anyone who happens to have a Hohner clavinet may adapt it to play
quarter tones by an invention of mine which is simply putting a device similar
to a bend bar on a guitar on the strings and hooking this up to a pedal. It's a
little primitive, but it can play quarter tones until a more satisfactory instru-
ment is available. Incidentally, with the foot pedal both hands are available
to play chords in quarter tones.

There are recent inventions in synthesizers which allow for infinite selection
of pitches and these can be used to play quarter tones.

33

CHAPTER 6

BASIC QUARTER TONE SCALES

If you will refer to the chart on page 15 you will see that there are 12 notes
available which are relatively "in tune" and out of these we may fashion a
number of scales. The 12 notes which I call the basic scale are:

BASIC SCALE

RATIO 1/1 12/11 9/8 11/9 4/3 11/8

16/11 3/2 18/11 16/9 11/6 64/33

34

The greatest deviation from pure or just intonation is plus or minus 3.9
cents. For example, A natural is 3.9 cents flat and F natural is 3.9 cents
sharp. This gives us a relatively in tune scale with which to operate. (It will
be more in tune than most equal tempered scales.) Of course there are an
infinitesimal variety of scales that can be made using quarter tones but for the
purpose of this book and for my own musical purposes I have decided to limit
the scales to the purest ratios.

If we divide the scale into two halves, the first half going from the tonic to the
fourth, the second half from the fifth (and quarter tone fifth) to the octave, we
get the following possibilities:

SEVEN TONE SCALES DERIVED FROM THE BASIC SCALE

36

Any line from Group A may be combined with any line from Group B to make a
7-tone scale. The following are examples of some of the possible scales de-
rived from the two halves of the basic scale:

SCALES DERIVED FROM THE TWO HALVES OF THE BASIC SCALE

A-1 B- 3

I suggest you play each scale ascending and descending. Then play each inter-
val in turn, test it and listen for the sound.

37

It is possible to derive other combinations of scales from the basic scales using
more or less notes than 7. For example:

SCALES USING MORE OR LESS THAN SEVEN NOTES

8 TONE

: 3 en ae

7 or 8 TONE

9 TONE

7 TONE "MAVERICK"

Se SS

38

CHAPTER 7

EXERCISES FOR DEXTERITY AND EAR TRAINING

Chromatic

39

ae ee eS

BOT Bt .6 ee 2 bee en ee

i
he
:
x
z
k
_

40

MAJOR SCALES

NOUS ee A I eS eal SR OE EG

en

GRE SIGEEEA-T\ 2 2144428
G01 D4 Oe eee Eee

41

42

28 ee eh ee ES Sf an a eee FY 2 er a

43

fa | Be 0S CS SSeS ESS SFE 7 PE 7 J
J | a ge Ze yer Le a 1 i hg VIR 22 SSS SSS
51 — |) pete | 0 EP TT ANN ES NE KROME ES BE i | A ee

ee See, 07

SA) SS See A
>< —___—__—_— SRR” ER RS TESS WATT SURG AEST DE Se AS BE A EE eS Se

3 Sa —_ i ns ee ee. ee
eee Sa ae Re Sa SRS ois ARS SP RES SRS a NG PR a OR
2 SS Se Se ee OS ST SS a Ce ee ee
2 AEA EE Re RE 3 Bag Be OS do A CREE Ab dle Cte At

44

lan

(AS TESS RR YW Ra sae Se
bh. 4 es

Se ee Ra ee eee eee eee
= SS ae SD, | 1 EY SE A, OE EE) EE gt SE Se aes oA Se

X

Ty (eo PSS SSR (SS Eee EE | ee
Ss A 2 eee A [Pj - — gg Sy SE SS

ae 3 a

72S SSS SSE ES RS RS I SS ES CO SEE a eS
a 0 sa tt
. RS SCD BE Dee Se ee ee OE a es “ al
OA SSE 20 SU SE EE SEE SS). _ SPITS KL SEO i 4

2 SO A eS

46

ao. SS Sa es
SSS Se ae ee | ee

=
———_ | he
shel) pay Y ove A _ _? ae oe er ae vey ey eso
V1 al We Le ee YN ee hee et

y

Saat ears en EE SS Ce
(oS ee ee ee ee a eee
a ae ee

J

4 —S ee

fo | ne yg oo eo Pea) $s er St tO

SE eas) es ee eee) A | 4h ok) |) | a ee

le WS“ RAY Mol Bee eee as) eee es) 2 6 ee ee ee eee ee ee eee ee ee

LY WY = PU EE I: We, MSs | ee Ee a ES DE I WT GS LR REGENT FS es eee
—____ — — —————

47

sc mm” A
2 | VP ff hel Uva ag 3 OYE

= SU SE es Be, A a a Pe
03 Sy a SS RE A RO A OC RT Be
y —— EE——— ——— a

kal -
Cp aS ee eee
SE BL Be ee one ee
OSE, Se RS
,

$$! SS OY EL oe a a 2 RE Ae ee.
F , :

SST ce soe een

OF 2 7 Seo Bee Be Den ee L

| Bh Ao Se ee
tt ’ :

48

CHROMATIC PATTERNS

They're real finger busters!

When you can do these patterns with any kind of speed you will really have your quarter-

tone fingerings mastered on your instrument.

fa Set) PS ey ET eS OS es A) Re RE ST IS Oe ee Ts ee | RR EC Pe eS ER ee

N
AL ES SS SS RY TS OS HS ee ee ne z=
° 7; ry 5 ; ; 5 ; b =

50

—

ee
2 oe) Seat BEES Jae es
UJ LW

— SE SE SS PT ET) GS rrSrny RRS PEER) Ga WES Soe
SP PT STR SE RE, See A ST ES RT) SO NS Oe CSE PTS FE OED SP ES GES BE ee (SSR es PS se oS ee Ee ) Mee
ee a) eae ea ees eee ae ee ee ie Ce Be ee
UC U ’ 4 U “ * 2 mi

Sou:
NO’ a
Gs

51

52

- _
(oS aes

4
, Mala Ages VS »« we Ue Vie Ve
WEE ed 2 AU Ee EE A

53

mes
A 2 ee OS RS SS TS) SP A PS GS
4 4.48) 44.44.48 S448 OO Fe 2 ee ee 2 eee ee se ee ee eee ee ee ee
¥ : : , . 77 ¥

54

CHORDAL PATTERNS

(Major Triads)

22S QELS 2 A A) A |S Ge Sn | OR es
SO) As RR TS ee a ee, ee a i ee
oo 2 SESE OE. A | EE Oh To 7 RE, ae | A ee Te ee

SS FE OE i i SD ee

56

ae | ~- JAR EY 2 a ae, BE 1 OS eet a EE Bee.
(a. a s,s ee ee ee ee

SB > Va ee he eM ee eR Tee Ag Re

Rage Ma 1 Le Ve

a
4
!
|
:
iS

7 SRS 26 GSE Pr ED Se ee.

57

he:

ne vi

(Minor Triads)

OSS EN SE _ ee PRwaT BESET

i
,
:
i
‘
i
,
‘
!

,
ree
ane

a i»

, i:

58

f

\ = —_ Sa Lo a — i
a. TET CW SS. Se 2 ee Ee ee eS ee eee ee ee
<a ee ee Oe ee eT ed te A. Oe eee oe eee eee
aS ee Se Bo Se ee SS ee Ee EP ed

— =o i
, COOREILP~ a Same OC Tos PASS eee ess 2 ST
to. Ge CR a Te A 1 iI PA AS SO <p gy tt 5 Pat
A eI a Se RE SS ee ES =. SS

aS, SO es

a
eS 6 eae Ge Fe ee

59

— ba

“Tr Bul

Pe | a 75 Sd Ae es: aD ieee,

<a

of

Te Ts |

at

et EE EE SE oe, A ER SESE | PE Ge SE

8? Ud Lh Va

<< ae Se ae ee ee

=
=
=
=~

2!) Soy ae EE A

| il
Sa ee

i > SS Sa 27 a Re be Seo
===" ST EL Pe

|
RT

:
=

60

et

aa CE Se ee
(a. SE + RSE 2 OE SS | SE

62

= : SSS
2 76 5 RS I ek eee

63

|
|
ft

64

ea bg hg ly EF

;
i
@
=
z
B

4
=

65

66

OS A ie

68

|
f
bs
d
i
3
|
i
J
|
i
|
lh
;

~

TSE +l Sess ee

oC SG Des ee oe, eS ee ee ee A ee

69

12

ES GRO” 00 4 ES! Te ES

ph
s system are

!

27 feels that the basic quarter tone

(The basic chords of Yasser

Essays Before A Sonata,

SSS 6S SE GET RS en. SESS SS See ER a (

in his book

!
il
il
|
|
ae
a
;
li
I!
lI,
il
k
|
if
fi
I

chords should have four or more notes which finds support in the theories of Jose

Yasser, an advocate of a 19-tone tuning.

Charles Ives,

74

75

RANDOM INTERVAL EXERCISES

76

"BASIC SCALES" 7”

5 eg SS SS

33
See pp. 34, 35,

78

"BASIC SCALE" COMBINATIONS

Combination of A and B

79

80

Transpose all scales to all keys. Also play all scales in this way.

81

NEW SCALES

The following are examples of some other scale possibilities which I have found most

nteresting.

Three equal 1/4 tones (see also no. 30, page 73).

SSS ee EE EE

’ az!

a _

7S 2 SS CS eS Ree es
3D 0 i Ee Ee oe ES RE
i .

ian
‘ME

=
»

82

Combination of two chords (see no. 32, p. 74).

CHAPTER 8
MELODIC STUDIES USING QUARTER TONES

STUDY 1

Saez m oie)
el Seen Cameos, eee ES Ue Se PS SS, OEE ) EEG acreee, BT WES SG ee 1 eee
i ES Sa TS ST FETS a 7” YS EE (SEES SE RE ODO ee eee
= Ce" Set ee 2 se ~
SS a =e ~—

. = oe,
(AN CSE RUNES TSN PRY 4 eI: ” ARON! AEE, ee) ye ee Rs ys | SES TE (SE en Ee (eee
SS SSS SS ee SE _ ed SE: PE OS LO ES es Se, eee

SS SS SS SSS ES Ceres) Sees a ee, | EE Ge, CE, A ee Se) Ge
— (eee SE Ee SSS SS Se) SESE. SEE eee
= _____.-____,____ ___
, Z ‘ aa
Y - | ‘QS NESS | SSS FS: eee ee oe ee ae ee
8 SS SD SO AEN | S OS | 2 SS ee SE
SS FESS an | oo EE ES? SEE ee _ Ee ie eee ee
a —_ a
ad
SS ——~ SST == a Ee eS =:
ST a. LM AS Re 7 ey EE, ee Bet SO? Cee SE ne (2 eee St
ES ES i a a Se | eS a) es 2 a a So i “ty —____—@ —}
Fecal = Ti ee

SE SS A A ES a A
~~

—

STUDY 2

85

STUDY 3

Medium - Legato

86

STUDY 4

e

cal

S)

cresc,

STUDY 5

Medium - without a sense of bar lines.
>= Listesso

+
"2 SP es ee ee a. 2 Gee
ek St 2 Le ee SE ee eT ee ae as
S08 Sy ees cee ES 9 WE | ee ee ee eT a A.
| ere ROR SEE | GS TH es
——

“ ——. toe Se OS ee

4
0 SS SE ES eT EO GS Sh. (SS WS (SS es TEE SSIS DAU S
ee Ee eee eee eee ea ee eee ee ee oe 2 ee eee Ae ee ee ee
a A ee le ee ee a ee
ee ee a ee ee eee

eee ee eS Ae ee Pa.
1 a a

ii]
=

D.C. al Fine

eo Thnk AY

88

STUDY 6

- Even 8ths -

Medium Rock

89

STUDY 7 (8th Notes)

Medium Fast - Staccato

Ss Sa aS SN ESTA (1 SESS TSR
7” eee eee oe ee ng st ee Pee ee
im OG Sete | 1 SE Se ee, ee ee

90

STUDY 8

Slowly - Broadly

91

- THE BLUES

STUDY 9

BIBLIOGRAPHY

Apel, Willi, Harvard Dictionary of Music, Cambridge, Mass.,
Harvard University Press, 1955.

Apel, Willi, Harvard Dictionary of Music, (2d Ed.), Cambridge, Mass.,
The Belknap Press of Harvard University, 1972.

Barbour, J. Murray, ‘Tuning and Equal Temperament, East Lansing,
Michigan, Michigan State College Press, 1953.

Busoni, Ferruccio, Sketch of a New Esthetic of Music, New York
G. Schirmer, Inc., 1911.

Helmholtz, Hermann, On The Sensations of Tone, New York
Dover Publications, Inc., 1954.

Ives, Charles, (ed. Howard Boatwright), Essays Before A Sonata
And Other Writings, New York,
W. W. Norton & Company, Inc., 1962.

Mayer, Max F., The Musicians Arithmetic; Drill Problems for an

Introduction to the Scientific Study of Musical Composition,
Columbia, Missouri, University of Missouri Press, 1929.

Musical Quarterly, Contemporary Art Music in Persia, New York,
G. Schirmer, Inc., Vol. LI, No. 4, October 1965.

Partch, Harry, Genesis of a Music: Monophony, Madison, Wisconsin,
The University of Wisconsin Press, 1949.

Read, Gardner, Music Notation, (2d Ed.), Boston
Allyn and Bacon, Inc., 9.

Reese, Gustave, Music in The Renaissance, New York,
W. W. Norton & Company, Inc., 1959.

Schillinger, Joseph, The Schillinger System of Musical Composition,
Vol. I, New York, Carl Fischer, Inc., 1941.

Strangways, A. H. Fox, The Music of Hindostan, Oxford,
The Clarendon Press, 1965; orig. 1914.

Toch, Ernst, The Shaping Forces in Music, New York
Criterion Music Corp., 1948.